Problem: The area that a rectangular garden is 24 square yards. List all feasible whole-number dimensions the garden have the right to have.

You are watching: The gcf of 12 and 20

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Solution: 1 yd x 24 yd, 2 yd x 12 yd, 3 yd x 8 yd, and also 4 yd x 6 yd

The whole-number size of this rectangular garden room the factors of the number 24. The adhering to statements deserve to be made about the factors of 24:

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and also 24 due to the fact that each of this numbers divides specifically into 24.The pairs that factors of 24 are: 1 and 24, 2 and 12, 3 and 8, and also 4 and 6.

To find the determinants of a whole number follow this procedure:

Keep dividing until a variable repeats.List all factors separated by commas.

Example 1: discover the components of 12.

Counting # DivisionFactor Pair
112 ÷ 1 = 121 x 12
212 ÷ 2 = 62 x 6
312 ÷ 3 = 43 x 4
412 ÷ 4 = 34 x 3 

Solution: The components of 12 room 1, 2, 3, 4, 6 and 12.

(Note: 

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 means that one or more factors has repeated therefore we prevent dividing.)

Example 2: discover the determinants of 20.

Counting #DivisionFactor Pair
120 ÷ 1 = 201 x 20
220 ÷ 2 = 102 x 10
320 ÷ 3 = 6 R2--------
420 ÷ 4 = 54 x 5
520 ÷ 5 = 45 x 4 

Solution: The determinants of 20 are 1, 2, 4, 5, 10 and also 20.

Example 3: find the components of 49.

Counting #DivisionFactor Pair
149 ÷ 1 = 491 x 49
249 ÷ 2 = 24 R1--------
349 ÷ 3 = 16 R1--------
449 ÷ 4 = 12 R1--------
549 ÷ 5 = 9 R4--------
649 ÷ 6 = 8 R1--------
749 ÷ 7 = 77 x 7 

Solution: The determinants of 49 room 1, 7 and 49

Problem: uncover the Greatest common Factor (GCF) that 12 and 20. (Note: place your mouse over the list of determinants below.)

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The typical factors the 12 and also 20 space 1, 2 and 4.

The greatest common variable of 12 and also 20 is 4.

Solution: GCF = 4

To uncover the Greatest typical Factor (GCF) of 2 or much more whole numbers, monitor this procedure:

Make a list of determinants for each whole number.Identify all factors that are typical to all lists.The Greatest common Factor (GCF) is the biggest of these usual factors.In examples 4 v 6, ar your computer mouse over the lists of determinants to see the usual factors.

Example 4: find the GCF of 24 and 36.

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The usual factors that 24 and also 36 room 1, 2, 3, 4, 6 and also 12.

The greatest common element of 24 and also 36 is 12.

Solution: GCF = 12

Example 5: find the GCF the 56 and also 63.

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The typical factors the 56 and also 63 space 1 and also 7.

The greatest common variable of 56 and also 63 is 7.

Solution: GCF = 7

Example 6: discover the GCF the 12, 30 and 54.

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The common factors of 12, 30 and 54 are 1, 2, 3 and 6.

The greatest common aspect of 12, 30 and also 54 is 6.

Solution: GCF = 6

Summary: The components of a entirety number space those numbers the divide specifically into that whole number. The Greatest typical Factor (GCF) that a collection of totality numbers is the largest factor usual to all totality numbers in the set.

Exercises

Directions: review each inquiry below. Click when in solution BOX and form in your answer; then click ENTER. After girlfriend click ENTER, a message will show up in the outcomes BOX to suggest whether her answer is exactly or incorrect. To begin over, click CLEAR.

1.Find the GCF the 18 and 36.ANSWER BOX: GCF =   

RESULTS BOX: 

2.Find the GCF of 30 and also 48.ANSWER BOX: GCF =   

RESULTS BOX: 

3.Find the GCF of 42 and 56.ANSWER BOX: GCF =   

RESULTS BOX: 

4.Find the GCF the 16, 48 and also 72.

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ANSWER BOX: GCF =   

RESULTS BOX: 

5.One rectangle-shaped garden has actually an area of 18 square meters. Another rectangular garden has an area that 81 square meters. What is the largest feasible whole-number dimension typical to both gardens?ANSWER BOX: GCF =  m  

RESULTS BOX: